Skip to main content
SpringerLink
Log in

n-median semilattices

  • Published:
Order Aims and scope Submit manuscript

Abstract

An n-median semilattice (n≥3) is a meet-semilattice such that (i) every principal ideal is a distributive lattice and (ii) any n-element set of elements is bounded above whenever each of its (n-1)-element subsets has an upper bound. A 3-median semilattice is thus a median semilattice in the classical sense. In this note we demonstrate how the characteristic features of median semilattices carry over to the more general case of n-median semilattices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • H.-J.Bandelt (1984) Discrete ordered sets whose covering graphs are median, Proc. Amer. Math. Soc. 91, 6–8.

    Google Scholar 

  • H.-J.Bandelt and A. W. M.Dress (1989) Weak hierarchies associated with similarity measures — an additive clustering technique, Bull. math. Biology 51, 133–166.

    Google Scholar 

  • H.-J. Bandelt and A. W. M. Dress (1990) A canonical decomposition theory for metrics on a finite set. Advances Math.: to appear.

  • H.-J.Bandelt and J.Hedlíková (1983) Median algebras, Discrete Math. 45, 1–30.

    Google Scholar 

  • H.-J.Bandelt and G. C.Meletiou (1990) An algebraic setting for near-unanimity consensus, Order 7, 169–178.

    Google Scholar 

  • J.-P. Barthélemy and M. F. Janowitz (1990) A formal theory of consensus, SIAM J. Discrete Math.: to appear.

  • J.-P.Barthélemy, B.Leclerc, and B.Monjardet (1986) On the use of ordered sets in problems of comparison and consensus of classifications, J. Classif. 3, 187–224.

    Google Scholar 

  • C. H.Cunkle (1963) Symmetric Boolean functions, Amer. Math. Soc. Monthly 70, 833–836.

    Google Scholar 

  • B. A. Davey, R. W. Quackenbush, and D. Schweigert (1988) Monotone clones and the varieties they determine. Preprint.

  • D.Duffus and I.Rival (1977) Path length in the covering graph of a lattice, Discrete Math. 19, 139–158.

    Google Scholar 

  • M. F.Janowitz (1991) A converse to the Sholander embedding, Discrete Math. 87, 315–318.

    Google Scholar 

  • F. R. McMorris and R. C. Powers (1990) Consensus weak hierarchies. Preprint.

  • M.Sholander (1954) Medians, lattices, and trees, Proc. Amer. Math. Soc. 5, 808–812.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Seminar, Universität Hamburg, Bundesstraße 55, D-2000, Hamburg, Germany

    Hans-Jürgen Bandelt

  2. Department of Mathematics and Statistics, University of Massachusetts, 01003, Amherst, MA, U.S.A.

    Melvin F. Janowitz

  3. Faculty of Agricultural Technology, T.E.I./M. at Arta, P.O. Box 110, GR-47100, Arta, Greece

    Gerasimos C. Meletiou

Authors
  1. Hans-Jürgen Bandelt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Melvin F. Janowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gerasimos C. Meletiou
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by I. G. Rosenberg

Research supported in part by ONR Grant N00014-90-1008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bandelt, HJ., Janowitz, M.F. & Meletiou, G.C. n-median semilattices. Order 8, 185–195 (1991). https://doi.org/10.1007/BF00383403

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00383403

AMS subject classification (1991)

Key words

Search

Navigation